Three-dimensional shape measurement of large-aperture aspheric mirrors by off-axis null Ronchi test

An off-axis null Ronchi test is presented to measure the three-dimensional (3D) shape of a large-aperture aspheric mirror. The method designs curved fringe patterns as null sinusoidal gratings by means of phase information and ray tracing. In the process of measurement, the curved fringe patterns are displayed on a transmission-type liquid crystal display (T-LCD) screen, and a CCD camera records the fringe patterns containing the information of deviations of the mirror. The slopes of the deviations of the mirror are obtained by using the recorded fringe patterns. The deviations are restored by integrating, and then the 3D shape of the mirror can be reconstructed. Compared with the classical null Ronchi test, the method can provide enough measured data points and avoid the jagged edges of bands on the null gratings. Moreover, the method can conveniently change period and direction of the curved fringes and accurately control phase shifting. Computer simulations and a preliminary experiment are presented to show the performance of the method.